The only Combat Command demo I can find is the Combat Command 2 demo from 2001. Is this close enough to get a good feel for this Combat Command game, or has it changed so much that the old demo wouldn't paint an accurate picture?

If it is the Palermo scenario demo then from a quick look it seems similar enough to give you an idea.

Graphics have been improved (though not radically changed) as per the screen shots on the product page and have been improved again in the initial patch. Palermo is a medium scale scenario in terms of map size and unit density there are both a number of smaller and larger scenarios available amongst those in CCME.

Overall though I think it should give you a good enough impression of the mechanics of CCME.